The Flux-Line Lattice in Superconductors

The Flux-Line Lattice in Superconductors

21 June 1995 | Ernst Helmut Brandt
The chapter discusses the flux-line lattice (FLL) in type-II superconductors, where magnetic flux can penetrate in the form of Abrikosov vortices, also known as flux lines or fluxons. These vortices arrange themselves into a triangular FLL, which is influenced by material inhomogeneities and thermal fluctuations in high-$T_c$ superconductors (HTSCs). The properties of the FLL are described by Ginzburg-Landau theory and electromagnetic London theory, with the vortex core treated as a singularity. In Nb alloys and HTSCs, the FLL is soft due to the large magnetic penetration depth, leading to dispersive elastic moduli and a softening effect. The anisotropy and layered structure of HTSCs further enhance this softening, potentially causing decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening can "melt" the FLL, leading to thermally activated depinning of flux lines or "pancake vortices" in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Despite achieving high critical currents, the small depinning energy prevents HTSCs from being used as conductors at high temperatures unless the applied current and magnetic field are small. The chapter also covers the observation of the FLL, the ideal FLL from Ginzburg-Landau and BCS theories, and the behavior of the FLL in anisotropic and layered superconductors.The chapter discusses the flux-line lattice (FLL) in type-II superconductors, where magnetic flux can penetrate in the form of Abrikosov vortices, also known as flux lines or fluxons. These vortices arrange themselves into a triangular FLL, which is influenced by material inhomogeneities and thermal fluctuations in high-$T_c$ superconductors (HTSCs). The properties of the FLL are described by Ginzburg-Landau theory and electromagnetic London theory, with the vortex core treated as a singularity. In Nb alloys and HTSCs, the FLL is soft due to the large magnetic penetration depth, leading to dispersive elastic moduli and a softening effect. The anisotropy and layered structure of HTSCs further enhance this softening, potentially causing decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening can "melt" the FLL, leading to thermally activated depinning of flux lines or "pancake vortices" in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Despite achieving high critical currents, the small depinning energy prevents HTSCs from being used as conductors at high temperatures unless the applied current and magnetic field are small. The chapter also covers the observation of the FLL, the ideal FLL from Ginzburg-Landau and BCS theories, and the behavior of the FLL in anisotropic and layered superconductors.
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